Several approaches exist to cure this kind of difficulties, one of which is built in the BHRY model presented by Ref. [1]}. As will be shown in Sec. REF , this model is constructed by including in the action all the possible terms of scaling dimension \(d+1\)  that are quadratic in the spin-2 field, weighted by coefficients that are treated as Lagrange multipliers. By fixing these coefficients one ensures the existence of a correct number of independent constraint equations that retain the physical degrees of freedom only. This process leads to the BHRY Lagrangian that contains a number of non-minimal couplings between the spin-2 field, the gauge field and gravity as well as a more involved kinetic sector:
\(\small \begin{split}\mathcal {L}_{BHRY} = &- \left|D_{\rho } B_{\mu \nu } \right|^2 + 2\left| D_{\mu } B^{\mu \nu }\right|^2 - \left[ D_{\mu } B^{*\mu \nu } D_{\nu } B + h.c. \right] \\& + \left| D_{\mu } B \right|^2 - m^2 \left( \left|B_{\mu \nu }\right|^2 - \left|B\right|^2 \right) + 2 R_{\mu \nu \rho \lambda } B^{*\mu \rho }B^{\nu \lambda } \\& - R_{\mu \nu } B^{*\mu \lambda } {B^{\nu }}_\lambda -\frac{1}{d+1} R \left|B\right|^2 -i q F_{\mu \nu } B^{*\mu \lambda } {B^{\nu }}_\lambda .\end{split}\) 
